Analytical solution of the DGLAP equations using the generating function method

Recently, we generated the evolution equations of the parton distribution functions (PDF) usually used in the hadrons phenomenology by the stochastic modeling of the non-equilibrium statistical mechanics in the momentum space. The evolution equations obtained from the stochastic modeling are the same as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, but they are acquired by a mathematical procedure based on the non-equilibrium statistical mechanics and Markov processes. In this paper, we present a new analytical solution of the parton evolution equation (DGLAP equation) for the non-singlet quark distribution function using the generating function method. This method is a general technique for solving the master equation of Markov processes.